Eigen Microstates Of Particle Gases For Passenger Flights In The United States

Flight delays occur around the world every day, which can bring substantial economic losses to airlines and cause chaos for air traffic and passengers. To reduce these negative impacts, we should find the statistical law of the flight system. By using the record of 20 years American domestic passenger flights among N airports, we define the instantaneous delay strength D-I, delay rate P, and microstate S-I which is a vector of length N. We establish the statistical ensemble through choosing M microstates at M different times t under the approximate delay rate. From this statistical ensemble, we can get the eigen microstates and the corresponding weight factors, which reflect the distribution of eigen microstates. Finally, we obtain the simulated delay rate P' = a . D-I . S-I . E-1 + b, where a and b are year-related parameters, E-1 is the eigen microstate of the largest weight factor and is a vector of length N. We use this formula to calculate (simulate) delay rate P' as a function of time t and find that the calculated (simulated) results agree very well with the observed real data P. Our approach can be extended to study other complex systems.Y